490 Yin, Vasilye¨a, and Pramanick
for a constant diameter single rod see Fig. 4c. filter design. fc is the cut-off frequency of the dominant mode and f is the center frequency of the filter to be designed. The curves have been obtained by the TLM analysis of the discontinuity using the MICROSTRIPE w4x program. The analytical equations for the curves are shown in the Appendix. The equations can be programmed in a personal computer and can be subsequently used as a direct aid to filter synthesis.
Figure 6 shows the computed K-inverter and phase w. curves for the constant diameter double rod see Fig. 4d. filter design. Here both K and w are functions of the distance d between the rods. The equations for the curves have been shown in the Appendix. Once again the curves and the equations can be directly used as design tools.
Figure 7 shows the design curves for single post filter with variable diameter and located at the center of the broad wall of the waveguide resonator as shown in Figure 4a. The corresponding design equations are shown in the Appendix. Our computed curves are more accurate than
Figure 6. Design curves for constant diameter and double rod filters.
Figure 7. Design cunes for variable diameter and single rod filters.
those in the Matthaei, Young, and Jones handbook w1x and the waveguide handbook of Marcuvitz w15x.
We have developed the design data for variable diameter double round rod discontinuities. However, the design equations based on the computed data are currently under preparation and are reported in the final journal version of the paper.
IV. RESULTS AND DISCUSSIONS
So far three filters have been designed using the modeling results developed and presented in the preceding section. The computed frequency responses of the filters show very good agreement and establish confidence in the method and the design curves.
Figure 8a shows the frequency response of variable diameter single rod filter centered at 9.5 GHz with 300 MHz bandwidth, 1 GHz isolation bandwidth, y70 dB isolation and 16 dB return
3D Simulators and Wa¨eguide Bandpass Filter Design |
491 |
Figure 8. a. Analyzed response of a single rod filter with variable diameter, a s 22.86 mm, b s 10.16 mm; rod radii: r1 s r7 s 0.785 mm, r2 s r6 s 2.169 mm, r3 s r5 s 2.413 mm, r4 s 2.444 mm; distances between rods: l1 s 20.761 mm, l2 s 23.353 mm, l3 s 23.731 mm.b. Analyzed response of a single rod filter with variable diameter, a s 22.86 mm, b s 10.16 mm; rod radii:
r1 s r7 s 1.018 mm, r2 s r6 s 2.490 mm, r3 s r5 s 2.730 mm, r4 s 2.761 mm; distances between rods:
l1 s 19.124 mm, l2 s 21.663 mm, l3 s 22.015 mm.
loss. This filter was designed as a constituent channel of an X-band diplexer. Figure 8b shows the response of the second channel designed by the foregoing method. The second channel is centered at a frequency which is 650 MHz away from the first channel but has an identical frequency response. Although the design models were derived using the FDTD method, the designed filters were analyzed using the finite element method w6x. The computed results show very good agreement between synthesis and analysis, except a difference of less than 2.00 dB in the passband return loss in one of the channel filters.
Figure 9 shows the responses of the designed channel filters using variable diameter double rods of a narrower band diplexer in which the filter passbands are centered at 9.55 and 10.65 GHz
Figure 9. a. Analyzed frequency response of a double rod filter with variable diameter, a s 22.86 mm,
b s 10.16 mm; rod radii: r1 s r5 s 0.536 mm, r2 s r4 |
|||
s 1.531 mm, r3 s |
1.634 mm; distances between rods: |
||
l1 s 21.210 mm, |
l |
2 s 23.036 mm. b. |
Analyzed fre- |
quency response |
of a double rod filter |
with variable |
|
diameter, a s 22.86 |
mm, b s 10.16 |
mm; |
rod |
radii: |
|
r1 s r5 s 0.634 |
mm, |
r2 s r4 s 1.638 |
mm, |
r3 s 1.736 |
|
mm, distances |
between rods: l1 s 19.655 |
mm, |
l2 s |
||
21.401 mm. |
|
|
|
|
|
with 100 MHz bandwidth and 1 GHz isolation bandwidth. These filters were analyzed using the mode matching method w12x. Once again, the agreement between design and analysis is found to be very good.
Figure 10 shows the analyzed frequency response of an X-band filter that used constant diameter single rod discontinuity. The filter is centered at 9.5 GHz with 300 MHz bandwidth, 1 GHz isolation bandwidth, y70 dB isolation and y16 dB return loss. The analysis was done using the TLM method and the MICROSTRIPE w4x program. The analysis of frequency response shows achievement of accurate center frequency and bandwidth. However, the return loss is y12.2 dB instead of y16 dB. In addition, the analyzed response does not show a Chebyshev type behavior. It shows well defined transmission zeros or pole extractions in the stopband. This is physically